Box$^2$EL: Concept and Role Box Embeddings for the Description Logic EL++

Representation learning in the form of semantic embeddings has been successfully applied to a variety of tasks in natural language processing and knowledge graphs. Recently, there has been growing interest in developing similar methods for learning embeddings of entire ontologies. We propose Box$^2$EL, a novel method for representation learning of ontologies in the Description Logic EL++, which represents both concepts and roles as boxes (i.e. axis-aligned hyperrectangles), such that the logical structure of the ontology is preserved. We theoretically prove the soundness of our model and conduct an extensive empirical evaluation, in which we achieve state-of-the-art results in subsumption prediction, link prediction, and deductive reasoning. As part of our evaluation, we introduce a novel benchmark for evaluating EL++ embedding models on predicting subsumptions involving both atomic and complex concepts.